常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题  

The Perturbed Poisson Risk Model with Constant Interest and a Threshold Dividend Strategy Under Absolute Ruin

作　　者：彭丹[1,2] 侯振挺[1] 刘再明[1] 

机构地区：[1]中南大学数学与统计学院,长沙410075 [2]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《应用数学学报》2012年第5期855-866,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10971230);教育部人文社会科学青年基金(10YJC630144)资助项目

摘　　要：本文考虑常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题,得到了累积分红现值的矩母函数,n阶原点矩所满足的积分-微分方程及边界条件;进一步得到了此模型下Gerber-Shiu折现罚函数所满足的积分-微分方程及相应边界条件,相应地将其转化为Volterra型积分方程,最后给出了索赔额为指数分布时绝对破产概率的解析表达式.In this paper, we study a perturbed Poisson risk model with constant inter- est and a threshold dividend strategy under absolute ruin. We derive integro-differential equations for the expectation of the discounted dividend payments, the moment generat- ing function with certain boundary conditions. Furthermore, we obtain integro-differential equations for the Gerber-Shiu discounted penalty function and transform them into Volterra integro equations. The explicit expression of the absolute ruin probability for exponential claim is also obtained.

关 键 词：绝对破产概率 利率 门限分红 积分-微分方程 Gerber-Shiu折现罚函数 

分 类 号：O212[理学—概率论与数理统计]